A GIS-Centric Optical Tracking System and Lap Simulator for Short Track SpeedSkating

Tom Landry∗, Langis Gagnon∗, Denis Laurendeau†∗Vision and Imaging team, CRIM, Montreal, Canada

tom.landry@crim.ca, langis.gagnon@crim.ca†Computer Vision and Systems Laboratory, Laval University, Quebec, Canada

laurend@gel.ulaval.ca

Abstract—This paper presents a GIS-centric computer vi-sion system for tracking high-speed skaters in competitionand training situations. This system outputs spatio-temporaltrajectories that are analyzed through presented geometric,physical and power-based models in order to evaluate sportsperformance. Through spatial SQL and shared database ac-cess, the GIS enables the manipulation of the trajectoriesand offer, amongst other, selection, fusion and completion oftracks, as well as automatic computation of distances betweencompetitors. We propose a new method for (1) calibratingthe cameras using a GIS-like image rectification method; 2)simulating trajectories and their associated power profiles tomodel the sport’s domain; 3) incorporating the instant centerof rotation in both the particle filter’s dynamic model and thesimulator and 4) leveraging several GIS advanced capabilitiesin a client-server application. Experimental results show thatour rectification methology is very precise, that our trackingperformance is acceptable and that the proposed power balancemodel is very close to the state of the art.

Keywords-tracking; camera calibration; segmentation; imagerectification; GIS;

I. INTRODUCTION

This work aims to automatically track the movement of

speed skaters on an indoor ice rink and to present this data

in a comprehensive and synthetized way to coaches. From

the computer vision point of view, several problems present

themselves: partial occlusions when skaters are very close

to each other; the size of the skaters range from about 20

by 20 pixels to 50 by 50 pixels; skaters are often tracked

simultaneously in two or more cameras; the calibration of

the cameras in such a large area. From a user-centric point of

view, the problems are related to the usability of the system;

manipulation, correction and management of the data series;

potential integration of external systems; creation of simple

yet useful tools to assess performance from trajectories.The remainder of this paper is organized as follows: the

next section explore the related work in sports. Section II is

the overview of the proposed system. Section IV explains

the camera calibration is carried out using GIS-style image

rectification. Section V describes the tracking method based

on particle filtering and introduces the notion of instant cen-

ter of rotation as a part of the dynamics model. Section VI

shows the geometric and power balance models of simulated

data that provides a basis for human performance assessment

on real data. Results of the tracking module are given in

section VII. A short discussion is presented in section VIII

before the conclusion of this paper.

II. RELATED WORK

There are several documented uses of video analysis

systems in sports. Early annotation-based systems were

conceived to analyze, amongst other, team plays, basic

motions and techniques, position on the field, speed or

acceleration. Barris and Button [1] identifies several appli-

cations of these systems, notably the planning of tactics and

strategies, the measurement of the team performance and

intervention efficiency, as well as the access to an early

cinematic retroaction. The major challenges cited are the

large raw data volume and the extraction of pertinent and

reliable information. Vincent [2] lists several data mining

and aggregation scenarios in various sports context.

The position of the athlete on the field can be obtained

by force plates, timing gates and wireless tags. For outdoor

sports, GPS receivers and inertial measurement units (IMU)

are often key elements [3], [4], [5]. For indoor sports, optical

tracking systems are often used. While systems relying on

markers are generally more precise, international regulations

often prohibit any modification to the equipment. Several

optical-based implementations exists for skating and in large

array of related sports [6], [7], [8], [9], [10], [11], [12], [13].

Using tracking data and video analysis, several models

can be devised. Van Ingen Schenau [15], [16] estimates

the friction forces of the air Fair [17], [18] and of the

ice Fice [19]. By using the power balance assumption, De

Koning [20], [21], [22] computes the optimal distribution of

work for cycling and 1500 meters speed skating. Efficiency

and energetic costs leading to optimal race conditions can

also be modeled by taking in account average power per

stroke or the overall technique [23], [24], [25], [26], [27],

[28].

III. OVERVIEW OF THE SYSTEM

The system is based on a star network of four GiGE

Prosilica GC650 cameras delivering 25 VGA frames per

second. The acquisition server launches four separate asyn-

chronous threads to store the uncompressed grabbed frame

2013 International Conference on Computer and Robot Vision

978-0-7695-4983-5/13 $26.00 © 2013 IEEE

DOI 10.1109/CRV.2013.11

288

on disk. A Omron CQM1 programmable logic controller

programmed in Ladder insures that all cameras are syn-

chronized by outputting a +/- 5V level on the camera input

pin to start or stop the data acquisition. In this fashion, all

sequences on disk contain the exact same number of frames.

Once saved on disk, the user can send requests for post-

processing to the server using a dedicated client application.

The four video sequences may be realigned and compressed

to a single, smaller, more manageable file. The other main

data processing is the particle filter optical tracking which

produces a series of localized detections called tracks. All

along those steps, intermediate results are stored in a central-

ized database linking the skating event and its competitors

to the video sequences and extracted tracking data.

The client application offers the possibility to drill down

in the database to select an event and playback its video

sequence. Manifold, a commercial geographical information

system (GIS) enables the manipulation of the associated

tracking information. It holds as a base layer an orthographic

referential closely duplicating the official skating rink of the

ISU. By the mean of spatial SQL scripts and native capa-

bilities, the GIS offer, amongst other, selection, fusion and

completion of tracks, automatic computation of distances

between competitors.

Most user-centric use cases covered by the present system

were related to data acquisition, visualization, manipulation

and management. These aspects were addressed as a map-

ping problem. The GIS was used to host a wide array of

functionalities, including pan and zoom, aggregation and

edition, free-hand measurement, track fusion, thematic for-

matting, labelling, and geospatial database interoperability.

Equipped with this toolbox, processed trajectories can be

more easily analysed according to their trajectories and

underlying dynamics.

The trajectories alone are not sufficient to assess the

performance of the athlete. A better basis is the power

deployed as it reaches several disciplines of sports science.

A non-accelerated parametric lap simulator, programmed in

Matlab, completes the system and is presented in section ??.

IV. CAMERA CALIBRATION

The ice rink dimension is 200 feet by 100 feet. Lenses

were chosen to cover a rectangular field of a view mapping

a little more than a quarter of the ice surface, resulting in

a field of view of about 44 meters. A 10% overlap zone is

present between the field of view of each camera. The height

of the structure housing the cameras of 68 feet, or about

22,5 meters, constitutes the distance to the subject. Sony’s

ICX424AL CCD sensor possess 659 effective pixels, each

measuring 7,4 microns, for a total CCD size of 4,88 mm.

Using the lenses Equation 1, the resulting focal distance is

3,2mm for a distance of 68 feet.

f =CCD × distance

width(1)

Zhang [29] camera calibration method was first consid-

ered. This method employs the pinhole camera model. By

observing a checkerboard pattern under different orienta-

tions, the intrinsic and extrinsic parameters are computed.

Figure 1. Result of the Zhang calibration method on a 1 meter widecheckerboard pattern used at the Pavillon de la Jeunesse, Quebec city.

Visually, this calibration method give good results, as

shown in Figure 1. Nevertheless, the input samples (Fig-

ure 2) provided were too correlated spatially. The calibration

pattern needs to be imaged under a variety of poses while

covering most of the sensor. This is mainly because the

pattern needs to be very large and the observation points

scattered around the arena. This specification could not be

met due to the limited physical access over the ice.

Figure 2. The image samples used as inputs to the Zhang method. Thesamples are closely correlated due to the environment.

A. Image rectificationOn the official speed skating rink, several features are

localized with precision, namely the starting and finish

lines, start corridors, inner rink and turn markers. Those

features are paired to the pixel coordinates of the camera

frames. As shown in figure 3, image rectification warps the

source image to the new referential by applying a high-order

polynomial transformation.Matlab’s warpPerspective and OpenCV’s imTransform

implementations were tested, but Manifold GIS rectification

289

Figure 3. Result of a 3rd order image rectification of the four input imagesover the orthographic referential in Manifold GIS.

was selected in order to lower the number of software

dependencies in the system and to improve design cohe-

siveness. The equation system of this type of polynomial

transformation is based on Equation 2.

x′ =I∑

i

∑J

jai,jx

iyj (2a)

y′ =I∑

i

∑J

jbi,jx

iyj (2b)

For all pairs of points, we have to find the coefficient ai,jet bi,j linking all points to their projection (x′,y′). As it is a

linear equation system, SVD factorization can be employed.

The color of the resulting pixels is then determined by

bilinear or bicubic interpolation.

B. Back-Projection errorThe RMS back-projection error is obtained by applying

the inverse transformation on a rectified image and by

determining the Euclidian distance between the new pixel

position and the original one. It therefore cumulates the

imprecision of both the direct and inverse transformation.

Figure 4 illustrates the magnitude of the errors on the ice

rink.In figure 4, we can see that RMS error grow rapidly

outside the area covered by control points, even diverging

near the sides. Inside the race corridors, for a 4th order

transformation, the RMS error is less than 1 pixel.

Table ITABLE OF THE RMS RECTIFICATION ERROR IN PIXELS, FOR THE FOUR

CAMERAS, FOR TRANSFORMATIONS OF 2nd , 3rd AND 4th ORDER.

Order Cam 0 Cam 1 Cam 2 Cam 3 Mean2 7.884 6.482 5.528 6.813 6.6763 4.394 3.436 3.545 3.201 3.6444 2.503 1.064 1.269 1.258 1.523

Control points 95 91 95 79 90

In Table I, we note that for a 4th order transformation,

the mean RMS error for all four cameras is 1,523 pixels.

Figure 4. From left to right, map of the RMS back-projection error inpixels, for the polynomial rectification of order 2, 3 and 4 of the four inputimages of the skating rink.

When excluding the outlier points outside the race corridors,

the average RMS error is reduced to approximately 0,447pixels. Assuming that half of this error is due to the direct

transformation, the mean RMS error for the race corridors

is reduced to 0,2235 pixels. By taking in account the image

resolution and the time delta, the uncertainty on instant

speeds due to the rectification process is ±0, 48 m/s, or

±1, 75 km/h.

V. OPTICAL TRACKING

Before being rectified onto the orthographic referential,

trajectories of the skaters need to be extracted from the video

sequences by optical tracking. Athletes are detected by a

background subtraction, modeled by their color distribution

and tracked by a particle filter.

A. Pre-processing

One of the most common way to estimate the foreground

of a sequence is by employing a mixture of Gaussians[30]

where each pixel is modeled independently. Tian [31] im-

proves the response to shadows and varying lighting con-

ditions. In the present research, the problem is very well

constrained. A simple subtraction is carried between the

current frame an empty background, obtained by averaging

several frames of the input sequence.

As shown in Figure 5, the foreground probability map

is binarized by Otsu’s [33] thresholding method. It is first

applied globally to the whole image to extract rough blobs,

then it applied locally in the neighbourhood of those blobs.

The resulting segmentation is less sensible to cast shadows.

This leads to a better tracking initialization.

B. Particle filtering

The particle filter, also named Condensation [34] al-

gorithm or sequential Monte Carlo approximation, is a

290

Figure 5. Foreground probability map obtained by subtraction (left), binarysegmentation of the map by Otsu’s thresholding method using the wholeimage (center) and a local region of interest (right).

common Bayesian technique often used in optical tracking

applications [35], [36], [37], [9], [34].

Observations are modeled by one or several character-

istics, such as shape, appearance, keypoints, texture or

color[38]. In speed skating, color can help locate the head

of the skater as every athlete in a competition is wearing a

bright yellow cap on its helmet. In most sports, countries

adopt unique color palettes on their suits. On one hand,

color not very discriminant in training because most of

the time, athletes are from the same country. On the other

hand, the sensitivity of color cameras tend to be much lower

than monochrome ones because of the presence of a Bayer

filter. In order to obtain a sharp image at a relatively high

framerate, the ambient lighting needs to be augmented. This

is not possible in a sports arena. Therefore, color information

was discarded in the overall solution.

The selected observation model is based on a simple 16-

bins histogram of grey levels [9], [10], [6]. This approach

is fast to compute and is robust to partial occlusions, but

perform badly in complex environments. In the current

application, the problem is relatively simple, the background

being a uniform sheet of ice.

Each particle is moved in state-space according to its

dynamic model. In order to predict the position of targets,

particle filters often defines autoregressive dynamic mod-

els [37], [9], [34] where the predicted position is inferred

from previous positions.

A 1st order model, also known as a random walk or a

Brownian motion, adds Gaussian noise N(0,Σ) to the last

known position xt−1. A 3rd order model predicts the posi-

tion xt by adding the displacement due to both the velocity

and to the acceleration to last known position, plus noise. In

the prediction phase, particles are propagated according to

either a 2nd and 3rd order model according to probabilities

P2nd and P3rd respectively, where 1− P2nd − P3rd > 0.

Observed short track speed skating trajectories are highly

constrained to the rink. Skaters are therefore most of the time

turning around a center of rotation. Instant center of rotation

are extracted by a sampling three equidistant points from the

trajectories and by applying a circular regression [39].

It can be seen on Figure 6 that instant centers of rotation

can be used to localize strokes, where the leg extension is

Figure 6. Clusters of instantaneous local centers of rotation (in green)indicate a turn (blue oval) and maximal extension during a stroke (redovals) for tracked data. A priori, the center of rotation during a turn isexpected to fall in the yellow oval.

maximal and where the optical center of mass is the furthest

from the overall trajectory.

To better capture the rotational motion of the skaters,

velocities and accelerations can be carried out in Euclidian

coordinates as well as polar coordinates. During the predic-

tion phase, the probability Pe that a skater is in a turn is

proportional to the distance of its instant center of rotation

relative to the expected center of rotation for this turn. With

higher values of Pe, the algorithm carries out the prediction

in polar coordinates instead of Euclidian coordinates. Instant

centers of rotation are also a key component in the physical

model that links speed, lean angle and centripetal force in

the simulator.

VI. SIMULATED DATA

Before power can be estimated from measured data or

used in the dynamic model of the tracking system, human

performance analysis is carried out for generated parametric

trajectories. In the current implementation, the simulation

does not interact with the optical tracking yet. It is provided

to Speed Skating Canada as a post-hoc analysis tool allowing

the modelisation of the domain.

The Figure 7 presents an accurate geometrical model. The

straight correspond approximately to the arc formed by the

exit D1 of a turn and the entry D3 of another, while passing

by the straight width D2. The lap generator receives five

input parameters:

• the turn radius r or corresponding to the segment

V 0V 2;

• the angle of entry θ formed between V 0V 1 and V 0V 2;

• the transition time t elapsed between the straight and

the turn, spanning over T0T1;

• the total lap time T ;

• the width of the straight w corresponding to segment

X0D2.

For each point along the generated parametric lap, several

physical properties are computed according to classical

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Figure 7. A non-accelerated parametric lap generated by the simulator. Ingreen is the trajectory of the skater, and in red, its instantaneous center ofrotation as determined by a circular regression [39].

mechanics, including the lean angle of the skater φ, the

centripetal force Fcent and the additional mass Madd felt

by the skater along the axis of its body.

Pt(t)− Pf (v) = dE/dt = M ∗ v ∗ a = 0 (3)

Pt(v) = Fskate ∗ v + Fair ∗ v (4)

The simulation is not accelerated. The variation of kinetic

energy dE/dt is therefore zero. The simulator takes in

account the friction forces Fice and Fair to compute instant

total power output Pt at every point using Equation 4. In

order to compute air friction Fair, the aerodynamic drag

coefficient CdA(v) used in the simulator was measured from

wind tunnel tests carried out by CNRC on three short track

speed skaters.

As a result, the average power output produced by the

simulator for a typical male skater is 261,64 Watts, against

256 Watts for Van Ingen Schenau [40]. Sources of internal

power loss, such as motion of the limbs, are difficult to

model. The simulated power output therefore only take in

account about 58% of the real power output. This scale

factor is an ad hoc value found in the literature that hasn’t

been fully validated.

VII. RESULTS

To assess the tracker performance, a ground truth of 1163

points, each measured two times, was acquired. A total of

15 independent trajectories of sufficient length was sampled.

The position of the point correspond to the center of mass of

the athlete, located approximatively between the belly button

and the coccyx.

Figure 8. Errors of the optical tracker for each of the nine Q quadrantsconsidered. The color of the points indicates error on instant velocity (EV)in pixels per frame, while the size of the points is proportional to the thesquare of the absolute error on position (EP) in pixels.

A mean error EP = 2.61 pixels was obtained for all

points produced by the tracking module. This relatively large

uncertainty is caused by shortcomings in the observation

model. Moreover, the filter tend to drift away from this

initial model at each iteration, even more when the skater’s

apppearance changes or when close to the maximal optical

distortion zones. When taking in account the mean error

on velocities EV = 0.79 pixels, EP seems to indicate a

systematic error between the optical center of mass and

the decision of an human. A human observer can use

hierarchical cues to assess the position of the center of mass,

such as limbs and head relative positions. The observation

model simply locates the skater by computing the optical

center of mass of its blob. In other words, whatever the

source, the location of the center of mass is consistent from

frame to frame, resulting in a small error on velocities.

The uncertainties on instant speeds due to positioning

error is ±1, 04 m/s or ±3, 76 km/h. When added to the rec-

tification error ER of ±1, 75 km/h claimed in section IV-B,

the overall uncertainty on velocities is ±5, 51 km/h, or about

12, 5% of the cruising speeds. This error is rather large

and implies that data series should be filtered before all

quantitative analysis.

VIII. DISCUSSION

The calibration procedure gave more than satisfactory

results. The protocol could be improved by automation of

some of the steps and by using more precise apparatus.

The optical tracker exhibits significant errors that can be

minimized by a more robust and modern filter, a better

observation model, a higher input resolution and and a more

elaborate interaction model between skaters, amongst others.

One of the main innovation of the developed model is the

use of instant rotation centers. This parameter allows the

computation of fictional forces which are a very important

cause of exhaustion in this sport. Apart from a more accurate

292

picture of the total power output, centers of rotation can also

be used to detect and measure the amplitude of strokes. This

data would prove useful in the creation of an accelerated

simulator.

A complete study of short track speed skating perfor-

mance requires a exhaustive modelisation of geometrical

[24], biomechanical, physiological and cinematic phenome-

nas. Once obtained on the basis of a single lap, this unified

model could be used to optimize the effort for a whole race

according to the athlete’s capacities and the race context.

IX. CONCLUSION

In this paper, we propose a novel GIS-centric computer

vision system for tracking speed skaters in competition and

training situations. We also propose the geometric, physi-

cal and power-based models and tools to evaluate human

performance.

The main problem remain the degradation of the tracking

performance when skaters are moving close to each other,

causing prolonged occlusion. In the future, it is assumed

that the inclusion of an accelerated power-based model in

the tracker’s dynamic model will improve prediction. By

providing a cleaner and more complete signal, an active

external positioning system would be highly recommended

to help develop accurate models. Moreover, as aerodynamic

drag is by far the most important factor in the power

output, future models would benefit from being realized in

collaboration with CNRC.

ACKNOWLEDGMENT

The author would like to thank Dr. Denis Laurendeau,

Laval University, and Dr. Langis Gagnon, CRIM, for their

direction and supervision. Thank you to Dr. Normand Teas-

dale, Laval University, for the invaluable scientific and

technical expertise. Thank you to Own The Podium and

Mitacs for the funding of a large part of this research. Special

thanks to M. Yves Hamelin, short track program director at

Speed skating Canada for the continous confidence, sense

of innovation and dedication to its sport.

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